ArtState
ArtState is an esoteric proglang sketch by User:Rdococ. The premise is that an image can represent a finite state machine by using colour channels to represent the positions of future possible states.
Execution
An ArtState program is a 32-bit RGBA bitmap image. Each pixel is a state with two transitions to other states, whose positions are described by the RG and BA channels respectively. The colour channels indicate signed offsets relative to the current pixel. Transitions past the edges of the image are looped.
A program may be run by tracking the current state and repeatedly asking the user which transition they want to follow. A black transparent pixel halts the program.
Computational Class
Programs can only accept two input symbols, but more can be imitated by adding intermediate states. States can only transition to other states within a 256x256 pixel area around them, so I think not even all FSA can be expressed.